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Q.

If f:RR is defined by f(x)={2sinxsin2x2xcosxifx0αforx=0  then the value of α so that f  is continuous at 0 is

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a

2

b

1

c

0

d

-1

answer is D.

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Detailed Solution

Ltx0f(x)=f(0)Ltx02sinxsin2x2xcosx=αLtx02sinx2sinxcosx2xcosx=αα=Ltx0tanxxLtx0sinxxα=11α=0

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If f:R→R is defined by f(x)={2sinx−sin2x2xcosxifx≠0αforx=0  then the value of α so that f  is continuous at 0 is